Strong convergence by a hybrid algorithm for finding a common fixed point of Lipschitz pseudocontraction and strict pseudocontraction in Hilbert spaces.

*(English)*Zbl 1297.47088Summary: We prove a strong convergence theorem by using a hybrid algorithm in order to find a common fixed point of a Lipschitz pseudocontraction and a \(\kappa\)-strict pseudocontraction in Hilbert spaces. Our results extend the recent ones announced by Y.-H. Yao et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 10, 4997–5002 (2009; Zbl 1222.47128)] and many others.

##### MSC:

47J25 | Iterative procedures involving nonlinear operators |

47H05 | Monotone operators and generalizations |

47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |

##### Keywords:

strong convergence; hybrid algorithm; common fixed point; Lipschitz pseudocontraction; \(\kappa\)-strict pseudocontraction; Hilbert space; pseudo-contractive mapping
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\textit{K. Ungchittrakool}, Abstr. Appl. Anal. 2011, Article ID 530683, 14 p. (2011; Zbl 1297.47088)

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